In a one-sample t-test, the sample mean exceeds the test value by 3, the sample standard deviation (calculated with divisor n − 1) is 6, and the value of the t-statistic is 2.5. The number of degrees of freedom of the test is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24
The one-sample t-statistic is
\( \displaystyle t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} = \frac{(\bar{x} - \mu_0)\sqrt{n}}{s} \)
Putting in the given values:
\( \displaystyle 2.5 = \frac{3\sqrt{n}}{6} \)
\( \sqrt{n} = 5 \), so n = 25
The degrees of freedom are
n − 1 = 25 − 1 = 24
Why the other options are incorrect
Option (1) 25 — Incorrect. 25 is the sample size n; the degrees of freedom are n − 1.
Option (3) 5 — Incorrect. 5 is \(\sqrt{n}\), not the degrees of freedom.
Option (4) 4 — Incorrect. This is \(\sqrt{n} - 1\); one must be subtracted from n, not from \(\sqrt{n}\).